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The total chromatic number χ T (G) of a graph G is the least number of colors needed to color the vertices and the edges of G such that no adjacent or incident pair of elements receive the same color.A simple graph G is called type 1 if χ T (G) = Δ(G) + 1, where Δ(G) is the maximum degree of G. In this paper we prove the following conjecture of Chen et al.: An (n - 2)-regular equibipartite...
It is well known that every non-cyclic group of order 8 possesses precisely 384 complete mappings (transversals). Here we explain why each of these groups possess the same number of complete mappings by deducing this number from the number of complete mappings of C 2 x C 2 .
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